• Re: Decidability Decider H [key Rice issue]

    From olcott@21:1/5 to Richard Damon on Mon Jul 3 16:40:08 2023
    XPost: comp.theory, sci.logic

    On 7/3/2023 4:34 PM, Richard Damon wrote:
    On 7/3/23 5:30 PM, olcott wrote:
    On 7/3/2023 4:07 PM, Richard Damon wrote:
    On 7/3/23 4:08 PM, olcott wrote:
    On 7/3/2023 2:58 PM, Richard Damon wrote:
    On 7/3/23 2:56 PM, olcott wrote:
    On 7/3/2023 1:25 PM, Richard Damon wrote:
    On 7/3/23 2:03 PM, olcott wrote:
    On 7/3/2023 11:26 AM, Richard Damon wrote:
    On 7/3/23 12:05 PM, olcott wrote:
    On 7/3/2023 10:58 AM, Richard Damon wrote:
    On 7/3/23 11:44 AM, olcott wrote:
    On 7/3/2023 10:35 AM, Richard Damon wrote:
    On 7/3/23 10:42 AM, olcott wrote:
    On 7/3/2023 8:13 AM, Richard Damon wrote:
    On 7/2/23 11:10 PM, olcott wrote:

    Only when I show you are wrong. Actually try to answer my >>>>>>>>>>>>>>> objections


    What about a three valued decider?
    0=undecidable
    1=halting
    2=not halting


    Doesn't meet the definition of a Halt Decider.


    Because these are semantic properties based on the behavior of >>>>>>>>>>>> the input it does refute Rice.

    Nope. Rice's theorem doesn't allow for an 'undecidable'
    output state either.

    Either the input is or is not something that is in the set >>>>>>>>>>> defined by the function/language defined.

    Undecidable is just admitting that Rice is true.


    Undecidable <is> a semantic property.

    Source of that Claim?

    And you aren't saying the Undecidable <IS> a semantic property, >>>>>>>>> but is an answer for if an input <HAS> some specific semantic >>>>>>>>> property.

    In computability theory, Rice's theorem states that all non-trivial >>>>>>>> semantic properties of programs are undecidable. A semantic
    property is
    one about the program's behavior
    https://en.wikipedia.org/wiki/Rice%27s_theorem

    Undecidable <is> a semantic property of the finite string pair: >>>>>>>> {H,D}.


    As I mentioned, many simple descriptions get it wrong. Note,
    later in the same page it says:

    It is important to note that Rice's theorem does not concern the >>>>>>> properties of machines or programs; it concerns properties of
    functions and languages.


    H correctly accepts every language specified by the pair: {H, *}
    (where the first element is the machine description of H and the
    second element is any other machine description) or rejects this
    pair as undecidable.



    So, you are admitting you don't understand what you are saying.

    D isn't "undecidable" but always has definite behavior based on the
    behavior of the definite machine H that it was based on (and thus
    you are being INTENTIONALLY dupicious by now calling H to be a some
    sort of other decider).

    Since you claim that Halt-Decider-H "Correctly" returned false for
    H(D,D) we know that D(D) Halts, so D the problem of D has an answer
    so hard to call "undecidable"

    Again, what is the definition of your "Language", and why do you
    call {H,D} as UNDECIDABLE, since H will be a FIXED DEFINED decider
    that is just WRONG about its input, that isn't "undecidable".

    {H,D} undecidable means that D is undecidable for H, which is an
    verified fact. The set of {H,*} finite string pairs do define a
    language.  Decidability <is> a semantic property because it
    can only be correctly decided on the basis of behavior.


    What do you mean by "Undecidable by H?"


    H correctly determines that it cannot provide a halt status
    consistent with the behavior of the directly executed D(D).

    So? If it REALLY could detect that, it just needs to give the opposite answer.

    Or, in other words, you are just admitting that H is wrong.

    Try and show how D could do that.
    D can loop if H says it will halt.
    D can halt when H says it will loop.

    How does D make itself decidable by H to contradict
    H determining that it is undecidable?


    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

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  • From Richard Damon@21:1/5 to olcott on Mon Jul 3 17:55:52 2023
    XPost: comp.theory, sci.logic

    On 7/3/23 5:40 PM, olcott wrote:
    On 7/3/2023 4:34 PM, Richard Damon wrote:
    On 7/3/23 5:30 PM, olcott wrote:
    On 7/3/2023 4:07 PM, Richard Damon wrote:
    On 7/3/23 4:08 PM, olcott wrote:
    On 7/3/2023 2:58 PM, Richard Damon wrote:
    On 7/3/23 2:56 PM, olcott wrote:
    On 7/3/2023 1:25 PM, Richard Damon wrote:
    On 7/3/23 2:03 PM, olcott wrote:
    On 7/3/2023 11:26 AM, Richard Damon wrote:
    On 7/3/23 12:05 PM, olcott wrote:
    On 7/3/2023 10:58 AM, Richard Damon wrote:
    On 7/3/23 11:44 AM, olcott wrote:
    On 7/3/2023 10:35 AM, Richard Damon wrote:
    On 7/3/23 10:42 AM, olcott wrote:
    On 7/3/2023 8:13 AM, Richard Damon wrote:
    On 7/2/23 11:10 PM, olcott wrote:

    Only when I show you are wrong. Actually try to answer >>>>>>>>>>>>>>>> my objections


    What about a three valued decider?
    0=undecidable
    1=halting
    2=not halting


    Doesn't meet the definition of a Halt Decider.


    Because these are semantic properties based on the behavior of >>>>>>>>>>>>> the input it does refute Rice.

    Nope. Rice's theorem doesn't allow for an 'undecidable' >>>>>>>>>>>> output state either.

    Either the input is or is not something that is in the set >>>>>>>>>>>> defined by the function/language defined.

    Undecidable is just admitting that Rice is true.


    Undecidable <is> a semantic property.

    Source of that Claim?

    And you aren't saying the Undecidable <IS> a semantic
    property, but is an answer for if an input <HAS> some specific >>>>>>>>>> semantic property.

    In computability theory, Rice's theorem states that all
    non-trivial
    semantic properties of programs are undecidable. A semantic
    property is
    one about the program's behavior
    https://en.wikipedia.org/wiki/Rice%27s_theorem

    Undecidable <is> a semantic property of the finite string pair: >>>>>>>>> {H,D}.


    As I mentioned, many simple descriptions get it wrong. Note,
    later in the same page it says:

    It is important to note that Rice's theorem does not concern the >>>>>>>> properties of machines or programs; it concerns properties of
    functions and languages.


    H correctly accepts every language specified by the pair: {H, *} >>>>>>> (where the first element is the machine description of H and the >>>>>>> second element is any other machine description) or rejects this >>>>>>> pair as undecidable.



    So, you are admitting you don't understand what you are saying.

    D isn't "undecidable" but always has definite behavior based on
    the behavior of the definite machine H that it was based on (and
    thus you are being INTENTIONALLY dupicious by now calling H to be
    a some sort of other decider).

    Since you claim that Halt-Decider-H "Correctly" returned false for >>>>>> H(D,D) we know that D(D) Halts, so D the problem of D has an
    answer so hard to call "undecidable"

    Again, what is the definition of your "Language", and why do you
    call {H,D} as UNDECIDABLE, since H will be a FIXED DEFINED decider >>>>>> that is just WRONG about its input, that isn't "undecidable".

    {H,D} undecidable means that D is undecidable for H, which is an
    verified fact. The set of {H,*} finite string pairs do define a
    language.  Decidability <is> a semantic property because it
    can only be correctly decided on the basis of behavior.


    What do you mean by "Undecidable by H?"


    H correctly determines that it cannot provide a halt status
    consistent with the behavior of the directly executed D(D).

    So? If it REALLY could detect that, it just needs to give the opposite
    answer.

    Or, in other words, you are just admitting that H is wrong.

    Try and show how D could do that.
    D can loop if H says it will halt.
    D can halt when H says it will loop.

    How does D make itself decidable by H to contradict
    H determining that it is undecidable?



    It doesn't need to, and the fact you are asking the question jkust shows
    you don't understand what you are talking about.

    You clearly don't understnad what "Decidability" means.

    Decidability isn't a property of an input or of an decider-input pair.

    If the value of the property isn't defined for the input, the property
    is improperrly defined. For D from your H, the Halting Property is fully defined, D(D) Halts (since H(D,D) returns 0).

    If a decider doesn't give the right answer for a given input, it is just
    wrong. There is no "could haves" as the decider is exactly what it is programmmed to be, so always does exactly what it is programmed to do,
    and the behavior of some other decider, even just slightly different
    than it is irrelevent to it.

    Thus, your claimed property isn't actually a valid property to try to
    decide.

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  • From olcott@21:1/5 to Richard Damon on Mon Jul 3 20:51:27 2023
    XPost: comp.theory, sci.logic

    On 7/3/2023 4:55 PM, Richard Damon wrote:
    On 7/3/23 5:40 PM, olcott wrote:
    On 7/3/2023 4:34 PM, Richard Damon wrote:
    On 7/3/23 5:30 PM, olcott wrote:
    On 7/3/2023 4:07 PM, Richard Damon wrote:
    On 7/3/23 4:08 PM, olcott wrote:
    On 7/3/2023 2:58 PM, Richard Damon wrote:
    On 7/3/23 2:56 PM, olcott wrote:
    On 7/3/2023 1:25 PM, Richard Damon wrote:
    On 7/3/23 2:03 PM, olcott wrote:
    On 7/3/2023 11:26 AM, Richard Damon wrote:
    On 7/3/23 12:05 PM, olcott wrote:
    On 7/3/2023 10:58 AM, Richard Damon wrote:
    On 7/3/23 11:44 AM, olcott wrote:
    On 7/3/2023 10:35 AM, Richard Damon wrote:
    On 7/3/23 10:42 AM, olcott wrote:
    On 7/3/2023 8:13 AM, Richard Damon wrote:
    On 7/2/23 11:10 PM, olcott wrote:

    Only when I show you are wrong. Actually try to answer >>>>>>>>>>>>>>>>> my objections


    What about a three valued decider?
    0=undecidable
    1=halting
    2=not halting


    Doesn't meet the definition of a Halt Decider.


    Because these are semantic properties based on the >>>>>>>>>>>>>> behavior of
    the input it does refute Rice.

    Nope. Rice's theorem doesn't allow for an 'undecidable' >>>>>>>>>>>>> output state either.

    Either the input is or is not something that is in the set >>>>>>>>>>>>> defined by the function/language defined.

    Undecidable is just admitting that Rice is true.


    Undecidable <is> a semantic property.

    Source of that Claim?

    And you aren't saying the Undecidable <IS> a semantic
    property, but is an answer for if an input <HAS> some
    specific semantic property.

    In computability theory, Rice's theorem states that all
    non-trivial
    semantic properties of programs are undecidable. A semantic >>>>>>>>>> property is
    one about the program's behavior
    https://en.wikipedia.org/wiki/Rice%27s_theorem

    Undecidable <is> a semantic property of the finite string
    pair: {H,D}.


    As I mentioned, many simple descriptions get it wrong. Note, >>>>>>>>> later in the same page it says:

    It is important to note that Rice's theorem does not concern >>>>>>>>> the properties of machines or programs; it concerns properties >>>>>>>>> of functions and languages.


    H correctly accepts every language specified by the pair: {H, *} >>>>>>>> (where the first element is the machine description of H and the >>>>>>>> second element is any other machine description) or rejects this >>>>>>>> pair as undecidable.



    So, you are admitting you don't understand what you are saying.

    D isn't "undecidable" but always has definite behavior based on
    the behavior of the definite machine H that it was based on (and >>>>>>> thus you are being INTENTIONALLY dupicious by now calling H to be >>>>>>> a some sort of other decider).

    Since you claim that Halt-Decider-H "Correctly" returned false
    for H(D,D) we know that D(D) Halts, so D the problem of D has an >>>>>>> answer so hard to call "undecidable"

    Again, what is the definition of your "Language", and why do you >>>>>>> call {H,D} as UNDECIDABLE, since H will be a FIXED DEFINED
    decider that is just WRONG about its input, that isn't
    "undecidable".

    {H,D} undecidable means that D is undecidable for H, which is an
    verified fact. The set of {H,*} finite string pairs do define a
    language.  Decidability <is> a semantic property because it
    can only be correctly decided on the basis of behavior.


    What do you mean by "Undecidable by H?"


    H correctly determines that it cannot provide a halt status
    consistent with the behavior of the directly executed D(D).

    So? If it REALLY could detect that, it just needs to give the
    opposite answer.

    Or, in other words, you are just admitting that H is wrong.

    Try and show how D could do that.
    D can loop if H says it will halt.
    D can halt when H says it will loop.

    How does D make itself decidable by H to contradict
    H determining that it is undecidable?



    It doesn't need to, and the fact you are asking the question jkust shows
    you don't understand what you are talking about.

    You clearly don't understnad what "Decidability" means.



    *Computable set*
    In computability theory, a set of natural numbers is called computable, recursive, or decidable if there is an algorithm which takes a number as
    input, terminates after a finite amount of time (possibly depending on
    the given number) and correctly decides whether the number belongs to
    the set or not. https://en.wikipedia.org/wiki/Computable_set

    Because A finite string can be construed as a very large integer the
    above must equally apply to finite strings. That you are trying to
    get away with disavowing this doesn't seem quite right. Since you only
    have an EE degree we could chalk this up to ignorance.

    It does seem that you acknowledge that there is no way to make
    decidability undecidable.


    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Mon Jul 3 23:22:15 2023
    XPost: comp.theory, sci.logic

    On 7/3/23 9:51 PM, olcott wrote:
    On 7/3/2023 4:55 PM, Richard Damon wrote:
    On 7/3/23 5:40 PM, olcott wrote:
    On 7/3/2023 4:34 PM, Richard Damon wrote:
    On 7/3/23 5:30 PM, olcott wrote:
    On 7/3/2023 4:07 PM, Richard Damon wrote:
    On 7/3/23 4:08 PM, olcott wrote:
    On 7/3/2023 2:58 PM, Richard Damon wrote:
    On 7/3/23 2:56 PM, olcott wrote:
    On 7/3/2023 1:25 PM, Richard Damon wrote:
    On 7/3/23 2:03 PM, olcott wrote:
    On 7/3/2023 11:26 AM, Richard Damon wrote:
    On 7/3/23 12:05 PM, olcott wrote:
    On 7/3/2023 10:58 AM, Richard Damon wrote:
    On 7/3/23 11:44 AM, olcott wrote:
    On 7/3/2023 10:35 AM, Richard Damon wrote:
    On 7/3/23 10:42 AM, olcott wrote:
    On 7/3/2023 8:13 AM, Richard Damon wrote:
    On 7/2/23 11:10 PM, olcott wrote:

    Only when I show you are wrong. Actually try to answer >>>>>>>>>>>>>>>>>> my objections


    What about a three valued decider?
    0=undecidable
    1=halting
    2=not halting


    Doesn't meet the definition of a Halt Decider. >>>>>>>>>>>>>>>>

    Because these are semantic properties based on the >>>>>>>>>>>>>>> behavior of
    the input it does refute Rice.

    Nope. Rice's theorem doesn't allow for an 'undecidable' >>>>>>>>>>>>>> output state either.

    Either the input is or is not something that is in the set >>>>>>>>>>>>>> defined by the function/language defined.

    Undecidable is just admitting that Rice is true.


    Undecidable <is> a semantic property.

    Source of that Claim?

    And you aren't saying the Undecidable <IS> a semantic
    property, but is an answer for if an input <HAS> some
    specific semantic property.

    In computability theory, Rice's theorem states that all
    non-trivial
    semantic properties of programs are undecidable. A semantic >>>>>>>>>>> property is
    one about the program's behavior
    https://en.wikipedia.org/wiki/Rice%27s_theorem

    Undecidable <is> a semantic property of the finite string >>>>>>>>>>> pair: {H,D}.


    As I mentioned, many simple descriptions get it wrong. Note, >>>>>>>>>> later in the same page it says:

    It is important to note that Rice's theorem does not concern >>>>>>>>>> the properties of machines or programs; it concerns properties >>>>>>>>>> of functions and languages.


    H correctly accepts every language specified by the pair: {H, *} >>>>>>>>> (where the first element is the machine description of H and the >>>>>>>>> second element is any other machine description) or rejects this >>>>>>>>> pair as undecidable.



    So, you are admitting you don't understand what you are saying. >>>>>>>>
    D isn't "undecidable" but always has definite behavior based on >>>>>>>> the behavior of the definite machine H that it was based on (and >>>>>>>> thus you are being INTENTIONALLY dupicious by now calling H to >>>>>>>> be a some sort of other decider).

    Since you claim that Halt-Decider-H "Correctly" returned false >>>>>>>> for H(D,D) we know that D(D) Halts, so D the problem of D has an >>>>>>>> answer so hard to call "undecidable"

    Again, what is the definition of your "Language", and why do you >>>>>>>> call {H,D} as UNDECIDABLE, since H will be a FIXED DEFINED
    decider that is just WRONG about its input, that isn't
    "undecidable".

    {H,D} undecidable means that D is undecidable for H, which is an >>>>>>> verified fact. The set of {H,*} finite string pairs do define a
    language.  Decidability <is> a semantic property because it
    can only be correctly decided on the basis of behavior.


    What do you mean by "Undecidable by H?"


    H correctly determines that it cannot provide a halt status
    consistent with the behavior of the directly executed D(D).

    So? If it REALLY could detect that, it just needs to give the
    opposite answer.

    Or, in other words, you are just admitting that H is wrong.

    Try and show how D could do that.
    D can loop if H says it will halt.
    D can halt when H says it will loop.

    How does D make itself decidable by H to contradict
    H determining that it is undecidable?



    It doesn't need to, and the fact you are asking the question jkust
    shows you don't understand what you are talking about.

    You clearly don't understnad what "Decidability" means.



    *Computable set*
    In computability theory, a set of natural numbers is called computable, recursive, or decidable if there is an algorithm which takes a number as input, terminates after a finite amount of time (possibly depending on
    the given number) and correctly decides whether the number belongs to
    the set or not. https://en.wikipedia.org/wiki/Computable_set

    Because A finite string can be construed as a very large integer the
    above must equally apply to finite strings. That you are trying to
    get away with disavowing this doesn't seem quite right. Since you only
    have an EE degree we could chalk this up to ignorance.

    It does seem that you acknowledge that there is no way to make
    decidability undecidable.



    Except that "Decidability" isn't a property of an "input"/Machine, but
    of a PROBLEM, or one of the sets you are talking about. (not MEMBERS of
    the set, which are the machines, but the set as a whole)>

    So, you are confusing a property of the SET with a property of the members.

    Decidability is about the ability for there to exist a machine that can
    decide if its input is a member of the set. If there exist such a
    machine, then the SET is computable/decidable. If not, the SET isn't computable/decidable.

    Nothing he talks about the possible members themselves being in the set
    or not being a property like "decidable", it just isn't a property of
    the members.

    Your question is like asking if 2 is Purple.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From olcott@21:1/5 to Richard Damon on Mon Jul 3 22:47:26 2023
    XPost: comp.theory, sci.logic

    On 7/3/2023 10:22 PM, Richard Damon wrote:
    On 7/3/23 9:51 PM, olcott wrote:
    On 7/3/2023 4:55 PM, Richard Damon wrote:
    On 7/3/23 5:40 PM, olcott wrote:
    On 7/3/2023 4:34 PM, Richard Damon wrote:
    On 7/3/23 5:30 PM, olcott wrote:
    On 7/3/2023 4:07 PM, Richard Damon wrote:
    On 7/3/23 4:08 PM, olcott wrote:
    On 7/3/2023 2:58 PM, Richard Damon wrote:
    On 7/3/23 2:56 PM, olcott wrote:
    On 7/3/2023 1:25 PM, Richard Damon wrote:
    On 7/3/23 2:03 PM, olcott wrote:
    On 7/3/2023 11:26 AM, Richard Damon wrote:
    On 7/3/23 12:05 PM, olcott wrote:
    On 7/3/2023 10:58 AM, Richard Damon wrote:
    On 7/3/23 11:44 AM, olcott wrote:
    On 7/3/2023 10:35 AM, Richard Damon wrote:
    On 7/3/23 10:42 AM, olcott wrote:
    On 7/3/2023 8:13 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>> On 7/2/23 11:10 PM, olcott wrote:

    Only when I show you are wrong. Actually try to >>>>>>>>>>>>>>>>>>> answer my objections


    What about a three valued decider?
    0=undecidable
    1=halting
    2=not halting


    Doesn't meet the definition of a Halt Decider. >>>>>>>>>>>>>>>>>

    Because these are semantic properties based on the >>>>>>>>>>>>>>>> behavior of
    the input it does refute Rice.

    Nope. Rice's theorem doesn't allow for an 'undecidable' >>>>>>>>>>>>>>> output state either.

    Either the input is or is not something that is in the >>>>>>>>>>>>>>> set defined by the function/language defined.

    Undecidable is just admitting that Rice is true. >>>>>>>>>>>>>>>

    Undecidable <is> a semantic property.

    Source of that Claim?

    And you aren't saying the Undecidable <IS> a semantic >>>>>>>>>>>>> property, but is an answer for if an input <HAS> some >>>>>>>>>>>>> specific semantic property.

    In computability theory, Rice's theorem states that all >>>>>>>>>>>> non-trivial
    semantic properties of programs are undecidable. A semantic >>>>>>>>>>>> property is
    one about the program's behavior
    https://en.wikipedia.org/wiki/Rice%27s_theorem

    Undecidable <is> a semantic property of the finite string >>>>>>>>>>>> pair: {H,D}.


    As I mentioned, many simple descriptions get it wrong. Note, >>>>>>>>>>> later in the same page it says:

    It is important to note that Rice's theorem does not concern >>>>>>>>>>> the properties of machines or programs; it concerns
    properties of functions and languages.


    H correctly accepts every language specified by the pair: {H, *} >>>>>>>>>> (where the first element is the machine description of H and the >>>>>>>>>> second element is any other machine description) or rejects this >>>>>>>>>> pair as undecidable.



    So, you are admitting you don't understand what you are saying. >>>>>>>>>
    D isn't "undecidable" but always has definite behavior based on >>>>>>>>> the behavior of the definite machine H that it was based on
    (and thus you are being INTENTIONALLY dupicious by now calling >>>>>>>>> H to be a some sort of other decider).

    Since you claim that Halt-Decider-H "Correctly" returned false >>>>>>>>> for H(D,D) we know that D(D) Halts, so D the problem of D has >>>>>>>>> an answer so hard to call "undecidable"

    Again, what is the definition of your "Language", and why do >>>>>>>>> you call {H,D} as UNDECIDABLE, since H will be a FIXED DEFINED >>>>>>>>> decider that is just WRONG about its input, that isn't
    "undecidable".

    {H,D} undecidable means that D is undecidable for H, which is an >>>>>>>> verified fact. The set of {H,*} finite string pairs do define a >>>>>>>> language.  Decidability <is> a semantic property because it
    can only be correctly decided on the basis of behavior.


    What do you mean by "Undecidable by H?"


    H correctly determines that it cannot provide a halt status
    consistent with the behavior of the directly executed D(D).

    So? If it REALLY could detect that, it just needs to give the
    opposite answer.

    Or, in other words, you are just admitting that H is wrong.

    Try and show how D could do that.
    D can loop if H says it will halt.
    D can halt when H says it will loop.

    How does D make itself decidable by H to contradict
    H determining that it is undecidable?



    It doesn't need to, and the fact you are asking the question jkust
    shows you don't understand what you are talking about.

    You clearly don't understnad what "Decidability" means.



    *Computable set*
    In computability theory, a set of natural numbers is called computable,
    recursive, or decidable if there is an algorithm which takes a number as
    input, terminates after a finite amount of time (possibly depending on
    the given number) and correctly decides whether the number belongs to
    the set or not. https://en.wikipedia.org/wiki/Computable_set

    Because A finite string can be construed as a very large integer the
    above must equally apply to finite strings. That you are trying to
    get away with disavowing this doesn't seem quite right. Since you only
    have an EE degree we could chalk this up to ignorance.

    It does seem that you acknowledge that there is no way to make
    decidability undecidable.



    Except that "Decidability" isn't a property of an "input"/Machine, but
    of a PROBLEM, or one of the sets you are talking about. (not MEMBERS of
    the set, which are the machines, but the set as a whole)>

    So, you are confusing a property of the SET with a property of the members.

    Decidability is about the ability for there to exist a machine that can decide if its input is a member of the set. If there exist such a
    machine, then the SET is computable/decidable. If not, the SET isn't computable/decidable.


    Since I just quoted that to you it is reasonable that you accept it.

    Nothing he talks about the possible members themselves being in the set
    or not being a property like "decidable", it just isn't a property of
    the members.


    Using Rogers' characterization of acceptable programming systems, Rice's theorem may essentially be generalized from Turing machines to most
    computer programming languages: there exists no automatic method that
    decides with generality non-trivial questions on the behavior of
    computer programs. https://en.wikipedia.org/wiki/Rice%27s_theorem

    H correctly determines whether or not it can correctly determine the
    halting status for all of the members of the set of conventional halting problem proof counter-examples and an infinite set of other elements.

    H is deciding the semantic property of its own behavior on a set of
    finite strings. The above says this can be done in C.

    Your question is like asking if 2 is Purple.

    Mere empty rhetoric utterly bereft of any supporting reasoning.



    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Tue Jul 4 00:06:52 2023
    XPost: comp.theory, sci.logic

    On 7/3/23 11:47 PM, olcott wrote:
    On 7/3/2023 10:22 PM, Richard Damon wrote:
    On 7/3/23 9:51 PM, olcott wrote:
    On 7/3/2023 4:55 PM, Richard Damon wrote:
    On 7/3/23 5:40 PM, olcott wrote:
    On 7/3/2023 4:34 PM, Richard Damon wrote:
    On 7/3/23 5:30 PM, olcott wrote:
    On 7/3/2023 4:07 PM, Richard Damon wrote:
    On 7/3/23 4:08 PM, olcott wrote:
    On 7/3/2023 2:58 PM, Richard Damon wrote:
    On 7/3/23 2:56 PM, olcott wrote:
    On 7/3/2023 1:25 PM, Richard Damon wrote:
    On 7/3/23 2:03 PM, olcott wrote:
    On 7/3/2023 11:26 AM, Richard Damon wrote:
    On 7/3/23 12:05 PM, olcott wrote:
    On 7/3/2023 10:58 AM, Richard Damon wrote:
    On 7/3/23 11:44 AM, olcott wrote:
    On 7/3/2023 10:35 AM, Richard Damon wrote:
    On 7/3/23 10:42 AM, olcott wrote:
    On 7/3/2023 8:13 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 7/2/23 11:10 PM, olcott wrote:

    Only when I show you are wrong. Actually try to >>>>>>>>>>>>>>>>>>>> answer my objections


    What about a three valued decider?
    0=undecidable
    1=halting
    2=not halting


    Doesn't meet the definition of a Halt Decider. >>>>>>>>>>>>>>>>>>

    Because these are semantic properties based on the >>>>>>>>>>>>>>>>> behavior of
    the input it does refute Rice.

    Nope. Rice's theorem doesn't allow for an 'undecidable' >>>>>>>>>>>>>>>> output state either.

    Either the input is or is not something that is in the >>>>>>>>>>>>>>>> set defined by the function/language defined.

    Undecidable is just admitting that Rice is true. >>>>>>>>>>>>>>>>

    Undecidable <is> a semantic property.

    Source of that Claim?

    And you aren't saying the Undecidable <IS> a semantic >>>>>>>>>>>>>> property, but is an answer for if an input <HAS> some >>>>>>>>>>>>>> specific semantic property.

    In computability theory, Rice's theorem states that all >>>>>>>>>>>>> non-trivial
    semantic properties of programs are undecidable. A semantic >>>>>>>>>>>>> property is
    one about the program's behavior
    https://en.wikipedia.org/wiki/Rice%27s_theorem

    Undecidable <is> a semantic property of the finite string >>>>>>>>>>>>> pair: {H,D}.


    As I mentioned, many simple descriptions get it wrong. Note, >>>>>>>>>>>> later in the same page it says:

    It is important to note that Rice's theorem does not concern >>>>>>>>>>>> the properties of machines or programs; it concerns
    properties of functions and languages.


    H correctly accepts every language specified by the pair: {H, *} >>>>>>>>>>> (where the first element is the machine description of H and the >>>>>>>>>>> second element is any other machine description) or rejects this >>>>>>>>>>> pair as undecidable.



    So, you are admitting you don't understand what you are saying. >>>>>>>>>>
    D isn't "undecidable" but always has definite behavior based >>>>>>>>>> on the behavior of the definite machine H that it was based on >>>>>>>>>> (and thus you are being INTENTIONALLY dupicious by now calling >>>>>>>>>> H to be a some sort of other decider).

    Since you claim that Halt-Decider-H "Correctly" returned false >>>>>>>>>> for H(D,D) we know that D(D) Halts, so D the problem of D has >>>>>>>>>> an answer so hard to call "undecidable"

    Again, what is the definition of your "Language", and why do >>>>>>>>>> you call {H,D} as UNDECIDABLE, since H will be a FIXED DEFINED >>>>>>>>>> decider that is just WRONG about its input, that isn't
    "undecidable".

    {H,D} undecidable means that D is undecidable for H, which is an >>>>>>>>> verified fact. The set of {H,*} finite string pairs do define a >>>>>>>>> language.  Decidability <is> a semantic property because it >>>>>>>>> can only be correctly decided on the basis of behavior.


    What do you mean by "Undecidable by H?"


    H correctly determines that it cannot provide a halt status
    consistent with the behavior of the directly executed D(D).

    So? If it REALLY could detect that, it just needs to give the
    opposite answer.

    Or, in other words, you are just admitting that H is wrong.

    Try and show how D could do that.
    D can loop if H says it will halt.
    D can halt when H says it will loop.

    How does D make itself decidable by H to contradict
    H determining that it is undecidable?



    It doesn't need to, and the fact you are asking the question jkust
    shows you don't understand what you are talking about.

    You clearly don't understnad what "Decidability" means.



    *Computable set*
    In computability theory, a set of natural numbers is called computable,
    recursive, or decidable if there is an algorithm which takes a number as >>> input, terminates after a finite amount of time (possibly depending on
    the given number) and correctly decides whether the number belongs to
    the set or not. https://en.wikipedia.org/wiki/Computable_set

    Because A finite string can be construed as a very large integer the
    above must equally apply to finite strings. That you are trying to
    get away with disavowing this doesn't seem quite right. Since you only
    have an EE degree we could chalk this up to ignorance.

    It does seem that you acknowledge that there is no way to make
    decidability undecidable.



    Except that "Decidability" isn't a property of an "input"/Machine, but
    of a PROBLEM, or one of the sets you are talking about. (not MEMBERS
    of the set, which are the machines, but the set as a whole)>

    So, you are confusing a property of the SET with a property of the
    members.

    Decidability is about the ability for there to exist a machine that
    can decide if its input is a member of the set. If there exist such a
    machine, then the SET is computable/decidable. If not, the SET isn't
    computable/decidable.


    Since I just quoted that to you it is reasonable that you accept it.

    Nope, Decidability is a property of PROBLEMS or SETS, not INPUTS.

    You can't seem to tell the diffence bcause of your ignorance.


    Nothing he talks about the possible members themselves being in the
    set or not being a property like "decidable", it just isn't a property
    of the members.


    Using Rogers' characterization of acceptable programming systems, Rice's theorem may essentially be generalized from Turing machines to most
    computer programming languages: there exists no automatic method that
    decides with generality non-trivial questions on the behavior of
    computer programs. https://en.wikipedia.org/wiki/Rice%27s_theorem

    Yes, it doesn't need to be about Turning Machines, but it is still about
    the ability to create a "program" to compute a Function / Decider for a Language/Set.


    H correctly determines whether or not it can correctly determine the
    halting status for all of the members of the set of conventional halting problem proof counter-examples and an infinite set of other elements.

    But that isn't a proper property.

    You don't have "Decidability" on individual inputs, so it isn't a
    Property of the input that can be decided on.


    H is deciding the semantic property of its own behavior on a set of
    finite strings. The above says this can be done in C.

    Nope, just shows you don't understand a thing about what you are saying.


    Your question is like asking if 2 is Purple.

    Mere empty rhetoric utterly bereft of any supporting reasoning.



    Nope, since "Decidability" isn't a property of a given input, trying to
    ask if a given input is Decidable is a simple category error.

    Your inability to understand that just highlights how ignorant you are
    of the whole field.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From olcott@21:1/5 to Richard Damon on Mon Jul 3 23:35:26 2023
    XPost: comp.theory, sci.logic

    On 7/3/2023 11:06 PM, Richard Damon wrote:
    On 7/3/23 11:47 PM, olcott wrote:
    On 7/3/2023 10:22 PM, Richard Damon wrote:
    On 7/3/23 9:51 PM, olcott wrote:
    On 7/3/2023 4:55 PM, Richard Damon wrote:
    On 7/3/23 5:40 PM, olcott wrote:
    On 7/3/2023 4:34 PM, Richard Damon wrote:
    On 7/3/23 5:30 PM, olcott wrote:
    On 7/3/2023 4:07 PM, Richard Damon wrote:
    On 7/3/23 4:08 PM, olcott wrote:
    On 7/3/2023 2:58 PM, Richard Damon wrote:
    On 7/3/23 2:56 PM, olcott wrote:
    On 7/3/2023 1:25 PM, Richard Damon wrote:
    On 7/3/23 2:03 PM, olcott wrote:
    On 7/3/2023 11:26 AM, Richard Damon wrote:
    On 7/3/23 12:05 PM, olcott wrote:
    On 7/3/2023 10:58 AM, Richard Damon wrote:
    On 7/3/23 11:44 AM, olcott wrote:
    On 7/3/2023 10:35 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>> On 7/3/23 10:42 AM, olcott wrote:
    On 7/3/2023 8:13 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>> On 7/2/23 11:10 PM, olcott wrote:

    Only when I show you are wrong. Actually try to >>>>>>>>>>>>>>>>>>>>> answer my objections


    What about a three valued decider?
    0=undecidable
    1=halting
    2=not halting


    Doesn't meet the definition of a Halt Decider. >>>>>>>>>>>>>>>>>>>

    Because these are semantic properties based on the >>>>>>>>>>>>>>>>>> behavior of
    the input it does refute Rice.

    Nope. Rice's theorem doesn't allow for an 'undecidable' >>>>>>>>>>>>>>>>> output state either.

    Either the input is or is not something that is in the >>>>>>>>>>>>>>>>> set defined by the function/language defined. >>>>>>>>>>>>>>>>>
    Undecidable is just admitting that Rice is true. >>>>>>>>>>>>>>>>>

    Undecidable <is> a semantic property.

    Source of that Claim?

    And you aren't saying the Undecidable <IS> a semantic >>>>>>>>>>>>>>> property, but is an answer for if an input <HAS> some >>>>>>>>>>>>>>> specific semantic property.

    In computability theory, Rice's theorem states that all >>>>>>>>>>>>>> non-trivial
    semantic properties of programs are undecidable. A >>>>>>>>>>>>>> semantic property is
    one about the program's behavior
    https://en.wikipedia.org/wiki/Rice%27s_theorem

    Undecidable <is> a semantic property of the finite string >>>>>>>>>>>>>> pair: {H,D}.


    As I mentioned, many simple descriptions get it wrong. >>>>>>>>>>>>> Note, later in the same page it says:

    It is important to note that Rice's theorem does not >>>>>>>>>>>>> concern the properties of machines or programs; it concerns >>>>>>>>>>>>> properties of functions and languages.


    H correctly accepts every language specified by the pair: >>>>>>>>>>>> {H, *}
    (where the first element is the machine description of H and >>>>>>>>>>>> the
    second element is any other machine description) or rejects >>>>>>>>>>>> this
    pair as undecidable.



    So, you are admitting you don't understand what you are saying. >>>>>>>>>>>
    D isn't "undecidable" but always has definite behavior based >>>>>>>>>>> on the behavior of the definite machine H that it was based >>>>>>>>>>> on (and thus you are being INTENTIONALLY dupicious by now >>>>>>>>>>> calling H to be a some sort of other decider).

    Since you claim that Halt-Decider-H "Correctly" returned >>>>>>>>>>> false for H(D,D) we know that D(D) Halts, so D the problem of >>>>>>>>>>> D has an answer so hard to call "undecidable"

    Again, what is the definition of your "Language", and why do >>>>>>>>>>> you call {H,D} as UNDECIDABLE, since H will be a FIXED
    DEFINED decider that is just WRONG about its input, that >>>>>>>>>>> isn't "undecidable".

    {H,D} undecidable means that D is undecidable for H, which is an >>>>>>>>>> verified fact. The set of {H,*} finite string pairs do define a >>>>>>>>>> language.  Decidability <is> a semantic property because it >>>>>>>>>> can only be correctly decided on the basis of behavior.


    What do you mean by "Undecidable by H?"


    H correctly determines that it cannot provide a halt status
    consistent with the behavior of the directly executed D(D).

    So? If it REALLY could detect that, it just needs to give the
    opposite answer.

    Or, in other words, you are just admitting that H is wrong.

    Try and show how D could do that.
    D can loop if H says it will halt.
    D can halt when H says it will loop.

    How does D make itself decidable by H to contradict
    H determining that it is undecidable?



    It doesn't need to, and the fact you are asking the question jkust
    shows you don't understand what you are talking about.

    You clearly don't understnad what "Decidability" means.



    *Computable set*
    In computability theory, a set of natural numbers is called computable, >>>> recursive, or decidable if there is an algorithm which takes a
    number as
    input, terminates after a finite amount of time (possibly depending on >>>> the given number) and correctly decides whether the number belongs to
    the set or not. https://en.wikipedia.org/wiki/Computable_set

    Because A finite string can be construed as a very large integer the
    above must equally apply to finite strings. That you are trying to
    get away with disavowing this doesn't seem quite right. Since you only >>>> have an EE degree we could chalk this up to ignorance.

    It does seem that you acknowledge that there is no way to make
    decidability undecidable.



    Except that "Decidability" isn't a property of an "input"/Machine,
    but of a PROBLEM, or one of the sets you are talking about. (not
    MEMBERS of the set, which are the machines, but the set as a whole)>

    So, you are confusing a property of the SET with a property of the
    members.

    Decidability is about the ability for there to exist a machine that
    can decide if its input is a member of the set. If there exist such a
    machine, then the SET is computable/decidable. If not, the SET isn't
    computable/decidable.


    Since I just quoted that to you it is reasonable that you accept it.

    Nope, Decidability is a property of PROBLEMS or SETS, not INPUTS.

    You can't seem to tell the diffence bcause of your ignorance.


    Nothing he talks about the possible members themselves being in the
    set or not being a property like "decidable", it just isn't a
    property of the members.


    Using Rogers' characterization of acceptable programming systems, Rice's
    theorem may essentially be generalized from Turing machines to most
    computer programming languages: there exists no automatic method that
    decides with generality non-trivial questions on the behavior of
    computer programs. https://en.wikipedia.org/wiki/Rice%27s_theorem

    Yes, it doesn't need to be about Turning Machines, but it is still about
    the ability to create a "program" to compute a Function / Decider for a Language/Set.


    H correctly determines whether or not it can correctly determine the
    halting status for all of the members of the set of conventional halting
    problem proof counter-examples and an infinite set of other elements.

    But that isn't a proper property.

    You don't have "Decidability" on individual inputs, so it isn't a
    Property of the input that can be decided on.

    H divides inputs into halting decidable and halting undecidable.


    H is deciding the semantic property of its own behavior on a set of
    finite strings. The above says this can be done in C.

    Nope, just shows you don't understand a thing about what you are saying.

    Any idiot can say that. Provide both reasoning and sources.


    Your question is like asking if 2 is Purple.

    Mere empty rhetoric utterly bereft of any supporting reasoning.



    Nope, since "Decidability" isn't a property of a given input, trying to
    ask if a given input is Decidable is a simple category error.


    Decidability is about the ability for there to exist a machine
    that can decide if its input is a member of the set.

    H decides an infinite set of elements that are halting decidable for H
    and another set that are halting undecidable for H.

    Your inability to understand that just highlights how ignorant you are
    of the whole field.

    I suspect that you might not have more than bluster and a penchant for rebuttal.

    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Tue Jul 4 09:27:09 2023
    XPost: comp.theory, sci.logic

    On 7/4/23 12:35 AM, olcott wrote:
    On 7/3/2023 11:06 PM, Richard Damon wrote:
    On 7/3/23 11:47 PM, olcott wrote:
    On 7/3/2023 10:22 PM, Richard Damon wrote:
    On 7/3/23 9:51 PM, olcott wrote:
    On 7/3/2023 4:55 PM, Richard Damon wrote:
    On 7/3/23 5:40 PM, olcott wrote:
    On 7/3/2023 4:34 PM, Richard Damon wrote:
    On 7/3/23 5:30 PM, olcott wrote:
    On 7/3/2023 4:07 PM, Richard Damon wrote:
    On 7/3/23 4:08 PM, olcott wrote:
    On 7/3/2023 2:58 PM, Richard Damon wrote:
    On 7/3/23 2:56 PM, olcott wrote:
    On 7/3/2023 1:25 PM, Richard Damon wrote:
    On 7/3/23 2:03 PM, olcott wrote:
    On 7/3/2023 11:26 AM, Richard Damon wrote:
    On 7/3/23 12:05 PM, olcott wrote:
    On 7/3/2023 10:58 AM, Richard Damon wrote:
    On 7/3/23 11:44 AM, olcott wrote:
    On 7/3/2023 10:35 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 7/3/23 10:42 AM, olcott wrote:
    On 7/3/2023 8:13 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>> On 7/2/23 11:10 PM, olcott wrote:

    Only when I show you are wrong. Actually try to >>>>>>>>>>>>>>>>>>>>>> answer my objections


    What about a three valued decider?
    0=undecidable
    1=halting
    2=not halting


    Doesn't meet the definition of a Halt Decider. >>>>>>>>>>>>>>>>>>>>

    Because these are semantic properties based on the >>>>>>>>>>>>>>>>>>> behavior of
    the input it does refute Rice.

    Nope. Rice's theorem doesn't allow for an
    'undecidable' output state either.

    Either the input is or is not something that is in the >>>>>>>>>>>>>>>>>> set defined by the function/language defined. >>>>>>>>>>>>>>>>>>
    Undecidable is just admitting that Rice is true. >>>>>>>>>>>>>>>>>>

    Undecidable <is> a semantic property.

    Source of that Claim?

    And you aren't saying the Undecidable <IS> a semantic >>>>>>>>>>>>>>>> property, but is an answer for if an input <HAS> some >>>>>>>>>>>>>>>> specific semantic property.

    In computability theory, Rice's theorem states that all >>>>>>>>>>>>>>> non-trivial
    semantic properties of programs are undecidable. A >>>>>>>>>>>>>>> semantic property is
    one about the program's behavior
    https://en.wikipedia.org/wiki/Rice%27s_theorem

    Undecidable <is> a semantic property of the finite string >>>>>>>>>>>>>>> pair: {H,D}.


    As I mentioned, many simple descriptions get it wrong. >>>>>>>>>>>>>> Note, later in the same page it says:

    It is important to note that Rice's theorem does not >>>>>>>>>>>>>> concern the properties of machines or programs; it >>>>>>>>>>>>>> concerns properties of functions and languages.


    H correctly accepts every language specified by the pair: >>>>>>>>>>>>> {H, *}
    (where the first element is the machine description of H >>>>>>>>>>>>> and the
    second element is any other machine description) or rejects >>>>>>>>>>>>> this
    pair as undecidable.



    So, you are admitting you don't understand what you are saying. >>>>>>>>>>>>
    D isn't "undecidable" but always has definite behavior based >>>>>>>>>>>> on the behavior of the definite machine H that it was based >>>>>>>>>>>> on (and thus you are being INTENTIONALLY dupicious by now >>>>>>>>>>>> calling H to be a some sort of other decider).

    Since you claim that Halt-Decider-H "Correctly" returned >>>>>>>>>>>> false for H(D,D) we know that D(D) Halts, so D the problem >>>>>>>>>>>> of D has an answer so hard to call "undecidable"

    Again, what is the definition of your "Language", and why do >>>>>>>>>>>> you call {H,D} as UNDECIDABLE, since H will be a FIXED >>>>>>>>>>>> DEFINED decider that is just WRONG about its input, that >>>>>>>>>>>> isn't "undecidable".

    {H,D} undecidable means that D is undecidable for H, which is an >>>>>>>>>>> verified fact. The set of {H,*} finite string pairs do define a >>>>>>>>>>> language.  Decidability <is> a semantic property because it >>>>>>>>>>> can only be correctly decided on the basis of behavior.


    What do you mean by "Undecidable by H?"


    H correctly determines that it cannot provide a halt status
    consistent with the behavior of the directly executed D(D).

    So? If it REALLY could detect that, it just needs to give the
    opposite answer.

    Or, in other words, you are just admitting that H is wrong.

    Try and show how D could do that.
    D can loop if H says it will halt.
    D can halt when H says it will loop.

    How does D make itself decidable by H to contradict
    H determining that it is undecidable?



    It doesn't need to, and the fact you are asking the question jkust >>>>>> shows you don't understand what you are talking about.

    You clearly don't understnad what "Decidability" means.



    *Computable set*
    In computability theory, a set of natural numbers is called
    computable,
    recursive, or decidable if there is an algorithm which takes a
    number as
    input, terminates after a finite amount of time (possibly depending on >>>>> the given number) and correctly decides whether the number belongs to >>>>> the set or not. https://en.wikipedia.org/wiki/Computable_set

    Because A finite string can be construed as a very large integer the >>>>> above must equally apply to finite strings. That you are trying to
    get away with disavowing this doesn't seem quite right. Since you only >>>>> have an EE degree we could chalk this up to ignorance.

    It does seem that you acknowledge that there is no way to make
    decidability undecidable.



    Except that "Decidability" isn't a property of an "input"/Machine,
    but of a PROBLEM, or one of the sets you are talking about. (not
    MEMBERS of the set, which are the machines, but the set as a whole)>

    So, you are confusing a property of the SET with a property of the
    members.

    Decidability is about the ability for there to exist a machine that
    can decide if its input is a member of the set. If there exist such
    a machine, then the SET is computable/decidable. If not, the SET
    isn't computable/decidable.


    Since I just quoted that to you it is reasonable that you accept it.

    Nope, Decidability is a property of PROBLEMS or SETS, not INPUTS.

    You can't seem to tell the diffence bcause of your ignorance.


    Nothing he talks about the possible members themselves being in the
    set or not being a property like "decidable", it just isn't a
    property of the members.


    Using Rogers' characterization of acceptable programming systems, Rice's >>> theorem may essentially be generalized from Turing machines to most
    computer programming languages: there exists no automatic method that
    decides with generality non-trivial questions on the behavior of
    computer programs. https://en.wikipedia.org/wiki/Rice%27s_theorem

    Yes, it doesn't need to be about Turning Machines, but it is still
    about the ability to create a "program" to compute a Function /
    Decider for a Language/Set.


    H correctly determines whether or not it can correctly determine the
    halting status for all of the members of the set of conventional halting >>> problem proof counter-examples and an infinite set of other elements.

    But that isn't a proper property.

    You don't have "Decidability" on individual inputs, so it isn't a
    Property of the input that can be decided on.

    H divides inputs into halting decidable and halting undecidable.

    Which means?

    After all, *ALL* inputs have a definite halting state, so there is a
    correct answer to them, so there always exists a decider that will get
    the right answer.

    It seems by your attempt at a definition, a "Decider" that just decides
    all machines are non-ha;ting would have all halting machines defined as undecidable.



    H is deciding the semantic property of its own behavior on a set of
    finite strings. The above says this can be done in C.

    Nope, just shows you don't understand a thing about what you are saying.

    Any idiot can say that. Provide both reasoning and sources.





    Your question is like asking if 2 is Purple.

    Mere empty rhetoric utterly bereft of any supporting reasoning.



    Nope, since "Decidability" isn't a property of a given input, trying
    to ask if a given input is Decidable is a simple category error.


       Decidability is about the ability for there to exist a machine
       that can decide if its input is a member of the set.

    H decides an infinite set of elements that are halting decidable for H
    and another set that are halting undecidable for H.

    Again, "Halting Decidable" is an improper term, as ALL machines are
    "Decidable" to halt by some machine. So there does exist a machine that
    will give the right answer. It is sometimes a different machine for
    different inputs.

    Read that definition again, and perhaps find a better source, as
    decidability is the ability for there to exist a machine that can
    decider FOR ANY INPUT, if that input is a member of the set.

    There ALWAYS exist a machine that will correctly indicate if a SPECIFIC
    input is a member of the set. Trivially, it can be one of two possible machines, Machine 1 always answers YES, Machine 2 always answers no. One
    of those machines is right. The key point is that you need to determine
    the answer for ALL inputs, thus it isn't a property of one of the
    inputs, but of the SET.

    As it is a property of the SET and not an input, there can't be
    'decider' to determine if an 'input' has that property, since inputs
    don't have that property, the set they are being tested for does.


    Your inability to understand that just highlights how ignorant you are
    of the whole field.

    I suspect that you might not have more than bluster and a penchant for rebuttal.


    Really, I guess that is just you projecting, because you describe
    yourself to the tee.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From olcott@21:1/5 to Richard Damon on Tue Jul 4 16:32:24 2023
    XPost: comp.theory, sci.logic

    On 7/4/2023 8:27 AM, Richard Damon wrote:
    On 7/4/23 12:35 AM, olcott wrote:
    On 7/3/2023 11:06 PM, Richard Damon wrote:
    On 7/3/23 11:47 PM, olcott wrote:
    On 7/3/2023 10:22 PM, Richard Damon wrote:
    On 7/3/23 9:51 PM, olcott wrote:
    On 7/3/2023 4:55 PM, Richard Damon wrote:
    On 7/3/23 5:40 PM, olcott wrote:
    On 7/3/2023 4:34 PM, Richard Damon wrote:
    On 7/3/23 5:30 PM, olcott wrote:
    On 7/3/2023 4:07 PM, Richard Damon wrote:
    On 7/3/23 4:08 PM, olcott wrote:
    On 7/3/2023 2:58 PM, Richard Damon wrote:
    On 7/3/23 2:56 PM, olcott wrote:
    On 7/3/2023 1:25 PM, Richard Damon wrote:
    On 7/3/23 2:03 PM, olcott wrote:
    On 7/3/2023 11:26 AM, Richard Damon wrote:
    On 7/3/23 12:05 PM, olcott wrote:
    On 7/3/2023 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>> On 7/3/23 11:44 AM, olcott wrote:
    On 7/3/2023 10:35 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>> On 7/3/23 10:42 AM, olcott wrote:
    On 7/3/2023 8:13 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/2/23 11:10 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>
    Only when I show you are wrong. Actually try to >>>>>>>>>>>>>>>>>>>>>>> answer my objections


    What about a three valued decider? >>>>>>>>>>>>>>>>>>>>>> 0=undecidable
    1=halting
    2=not halting


    Doesn't meet the definition of a Halt Decider. >>>>>>>>>>>>>>>>>>>>>

    Because these are semantic properties based on the >>>>>>>>>>>>>>>>>>>> behavior of
    the input it does refute Rice.

    Nope. Rice's theorem doesn't allow for an >>>>>>>>>>>>>>>>>>> 'undecidable' output state either.

    Either the input is or is not something that is in >>>>>>>>>>>>>>>>>>> the set defined by the function/language defined. >>>>>>>>>>>>>>>>>>>
    Undecidable is just admitting that Rice is true. >>>>>>>>>>>>>>>>>>>

    Undecidable <is> a semantic property.

    Source of that Claim?

    And you aren't saying the Undecidable <IS> a semantic >>>>>>>>>>>>>>>>> property, but is an answer for if an input <HAS> some >>>>>>>>>>>>>>>>> specific semantic property.

    In computability theory, Rice's theorem states that all >>>>>>>>>>>>>>>> non-trivial
    semantic properties of programs are undecidable. A >>>>>>>>>>>>>>>> semantic property is
    one about the program's behavior
    https://en.wikipedia.org/wiki/Rice%27s_theorem >>>>>>>>>>>>>>>>
    Undecidable <is> a semantic property of the finite >>>>>>>>>>>>>>>> string pair: {H,D}.


    As I mentioned, many simple descriptions get it wrong. >>>>>>>>>>>>>>> Note, later in the same page it says:

    It is important to note that Rice's theorem does not >>>>>>>>>>>>>>> concern the properties of machines or programs; it >>>>>>>>>>>>>>> concerns properties of functions and languages.


    H correctly accepts every language specified by the pair: >>>>>>>>>>>>>> {H, *}
    (where the first element is the machine description of H >>>>>>>>>>>>>> and the
    second element is any other machine description) or >>>>>>>>>>>>>> rejects this
    pair as undecidable.



    So, you are admitting you don't understand what you are >>>>>>>>>>>>> saying.

    D isn't "undecidable" but always has definite behavior >>>>>>>>>>>>> based on the behavior of the definite machine H that it was >>>>>>>>>>>>> based on (and thus you are being INTENTIONALLY dupicious by >>>>>>>>>>>>> now calling H to be a some sort of other decider).

    Since you claim that Halt-Decider-H "Correctly" returned >>>>>>>>>>>>> false for H(D,D) we know that D(D) Halts, so D the problem >>>>>>>>>>>>> of D has an answer so hard to call "undecidable"

    Again, what is the definition of your "Language", and why >>>>>>>>>>>>> do you call {H,D} as UNDECIDABLE, since H will be a FIXED >>>>>>>>>>>>> DEFINED decider that is just WRONG about its input, that >>>>>>>>>>>>> isn't "undecidable".

    {H,D} undecidable means that D is undecidable for H, which >>>>>>>>>>>> is an
    verified fact. The set of {H,*} finite string pairs do define a >>>>>>>>>>>> language.  Decidability <is> a semantic property because it >>>>>>>>>>>> can only be correctly decided on the basis of behavior. >>>>>>>>>>>>

    What do you mean by "Undecidable by H?"


    H correctly determines that it cannot provide a halt status >>>>>>>>>> consistent with the behavior of the directly executed D(D). >>>>>>>>>
    So? If it REALLY could detect that, it just needs to give the >>>>>>>>> opposite answer.

    Or, in other words, you are just admitting that H is wrong.

    Try and show how D could do that.
    D can loop if H says it will halt.
    D can halt when H says it will loop.

    How does D make itself decidable by H to contradict
    H determining that it is undecidable?



    It doesn't need to, and the fact you are asking the question
    jkust shows you don't understand what you are talking about.

    You clearly don't understnad what "Decidability" means.



    *Computable set*
    In computability theory, a set of natural numbers is called
    computable,
    recursive, or decidable if there is an algorithm which takes a
    number as
    input, terminates after a finite amount of time (possibly
    depending on
    the given number) and correctly decides whether the number belongs to >>>>>> the set or not. https://en.wikipedia.org/wiki/Computable_set

    Because A finite string can be construed as a very large integer the >>>>>> above must equally apply to finite strings. That you are trying to >>>>>> get away with disavowing this doesn't seem quite right. Since you
    only
    have an EE degree we could chalk this up to ignorance.

    It does seem that you acknowledge that there is no way to make
    decidability undecidable.



    Except that "Decidability" isn't a property of an "input"/Machine,
    but of a PROBLEM, or one of the sets you are talking about. (not
    MEMBERS of the set, which are the machines, but the set as a whole)> >>>>>
    So, you are confusing a property of the SET with a property of the
    members.

    Decidability is about the ability for there to exist a machine that
    can decide if its input is a member of the set. If there exist such
    a machine, then the SET is computable/decidable. If not, the SET
    isn't computable/decidable.


    Since I just quoted that to you it is reasonable that you accept it.

    Nope, Decidability is a property of PROBLEMS or SETS, not INPUTS.

    You can't seem to tell the diffence bcause of your ignorance.


    Nothing he talks about the possible members themselves being in the
    set or not being a property like "decidable", it just isn't a
    property of the members.


    Using Rogers' characterization of acceptable programming systems,
    Rice's
    theorem may essentially be generalized from Turing machines to most
    computer programming languages: there exists no automatic method that
    decides with generality non-trivial questions on the behavior of
    computer programs. https://en.wikipedia.org/wiki/Rice%27s_theorem

    Yes, it doesn't need to be about Turning Machines, but it is still
    about the ability to create a "program" to compute a Function /
    Decider for a Language/Set.


    H correctly determines whether or not it can correctly determine the
    halting status for all of the members of the set of conventional
    halting
    problem proof counter-examples and an infinite set of other elements.

    But that isn't a proper property.

    You don't have "Decidability" on individual inputs, so it isn't a
    Property of the input that can be decided on.

    H divides inputs into halting decidable and halting undecidable.

    Which means?

    After all, *ALL* inputs have a definite halting state, so there is a
    correct answer to them, so there always exists a decider that will get
    the right answer.

    It seems by your attempt at a definition, a "Decider" that just decides
    all machines are non-ha;ting would have all halting machines defined as undecidable.

    I never said anything like that.
    (Here is what I already said)
    H returns three values:

    0=halting is undecidable by H
    1=halting
    2=not halting

    The human user runs H(D,D) and H returns 0. This tells the human
    user to run H1(D,D) to get the correct halt status decision for H.
    Because D could not have reconfigured itself this must work correctly.



    H is deciding the semantic property of its own behavior on a set of
    finite strings. The above says this can be done in C.

    Nope, just shows you don't understand a thing about what you are saying.

    Any idiot can say that. Provide both reasoning and sources.





    Your question is like asking if 2 is Purple.

    Mere empty rhetoric utterly bereft of any supporting reasoning.



    Nope, since "Decidability" isn't a property of a given input, trying
    to ask if a given input is Decidable is a simple category error.


        Decidability is about the ability for there to exist a machine
        that can decide if its input is a member of the set.

    H decides an infinite set of elements that are halting decidable for H
    and another set that are halting undecidable for H.

    Again, "Halting Decidable" is an improper term,

    It is a brand new concept that was never relevant before because
    everyone incorrectly assumed that deciding halting decidability
    was blocked by Rice.

    H correctly divides its inputs into those having the pathological
    relationship to H of the conventional halting problem proofs and
    inputs that do not have this relationship.

    as ALL machines are
    "Decidable" to halt by some machine. So there does exist a machine that
    will give the right answer. It is sometimes a different machine for
    different inputs.

    Read that definition again, and perhaps find a better source, as
    decidability is the ability for there to exist a machine that can
    decider FOR ANY INPUT, if that input is a member of the set.


    My current code can already do that for every member of the set.

    There ALWAYS exist a machine that will correctly indicate if a SPECIFIC
    input is a member of the set. Trivially, it can be one of two possible machines, Machine 1 always answers YES, Machine 2 always answers no. One
    of those machines is right. The key point is that you need to determine
    the answer for ALL inputs, thus it isn't a property of one of the
    inputs, but of the SET.


    My code also rejects inputs that are not members of this set.

    As it is a property of the SET and not an input, there can't be
    'decider' to determine if an 'input' has that property, since inputs
    don't have that property, the set they are being tested for does.


    I had very recent very long discussions with a PhD computer scientist
    and he seemed to believe that the halting problem is about dividing
    finite string pairs into those that halt on their input and those that
    do not.

    My case is analogous. H divides finite strings into those that have a pathological relationship to H and those that do not on the basis of the behavior that this finite string specifies.


    Your inability to understand that just highlights how ignorant you
    are of the whole field.

    I suspect that you might not have more than bluster and a penchant for
    rebuttal.


    Really, I guess that is just you projecting, because you describe
    yourself to the tee.




    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Tue Jul 4 19:00:29 2023
    XPost: comp.theory, sci.logic

    On 7/4/23 5:32 PM, olcott wrote:
    On 7/4/2023 8:27 AM, Richard Damon wrote:
    On 7/4/23 12:35 AM, olcott wrote:
    On 7/3/2023 11:06 PM, Richard Damon wrote:
    On 7/3/23 11:47 PM, olcott wrote:
    On 7/3/2023 10:22 PM, Richard Damon wrote:
    On 7/3/23 9:51 PM, olcott wrote:
    On 7/3/2023 4:55 PM, Richard Damon wrote:
    On 7/3/23 5:40 PM, olcott wrote:
    On 7/3/2023 4:34 PM, Richard Damon wrote:
    On 7/3/23 5:30 PM, olcott wrote:
    On 7/3/2023 4:07 PM, Richard Damon wrote:
    On 7/3/23 4:08 PM, olcott wrote:
    On 7/3/2023 2:58 PM, Richard Damon wrote:
    On 7/3/23 2:56 PM, olcott wrote:
    On 7/3/2023 1:25 PM, Richard Damon wrote:
    On 7/3/23 2:03 PM, olcott wrote:
    On 7/3/2023 11:26 AM, Richard Damon wrote:
    On 7/3/23 12:05 PM, olcott wrote:
    On 7/3/2023 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 7/3/23 11:44 AM, olcott wrote:
    On 7/3/2023 10:35 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>> On 7/3/23 10:42 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/3/2023 8:13 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/2/23 11:10 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>
    Only when I show you are wrong. Actually try to >>>>>>>>>>>>>>>>>>>>>>>> answer my objections


    What about a three valued decider? >>>>>>>>>>>>>>>>>>>>>>> 0=undecidable
    1=halting
    2=not halting


    Doesn't meet the definition of a Halt Decider. >>>>>>>>>>>>>>>>>>>>>>

    Because these are semantic properties based on the >>>>>>>>>>>>>>>>>>>>> behavior of
    the input it does refute Rice.

    Nope. Rice's theorem doesn't allow for an >>>>>>>>>>>>>>>>>>>> 'undecidable' output state either.

    Either the input is or is not something that is in >>>>>>>>>>>>>>>>>>>> the set defined by the function/language defined. >>>>>>>>>>>>>>>>>>>>
    Undecidable is just admitting that Rice is true. >>>>>>>>>>>>>>>>>>>>

    Undecidable <is> a semantic property.

    Source of that Claim?

    And you aren't saying the Undecidable <IS> a semantic >>>>>>>>>>>>>>>>>> property, but is an answer for if an input <HAS> some >>>>>>>>>>>>>>>>>> specific semantic property.

    In computability theory, Rice's theorem states that all >>>>>>>>>>>>>>>>> non-trivial
    semantic properties of programs are undecidable. A >>>>>>>>>>>>>>>>> semantic property is
    one about the program's behavior
    https://en.wikipedia.org/wiki/Rice%27s_theorem >>>>>>>>>>>>>>>>>
    Undecidable <is> a semantic property of the finite >>>>>>>>>>>>>>>>> string pair: {H,D}.


    As I mentioned, many simple descriptions get it wrong. >>>>>>>>>>>>>>>> Note, later in the same page it says:

    It is important to note that Rice's theorem does not >>>>>>>>>>>>>>>> concern the properties of machines or programs; it >>>>>>>>>>>>>>>> concerns properties of functions and languages. >>>>>>>>>>>>>>>>

    H correctly accepts every language specified by the pair: >>>>>>>>>>>>>>> {H, *}
    (where the first element is the machine description of H >>>>>>>>>>>>>>> and the
    second element is any other machine description) or >>>>>>>>>>>>>>> rejects this
    pair as undecidable.



    So, you are admitting you don't understand what you are >>>>>>>>>>>>>> saying.

    D isn't "undecidable" but always has definite behavior >>>>>>>>>>>>>> based on the behavior of the definite machine H that it >>>>>>>>>>>>>> was based on (and thus you are being INTENTIONALLY >>>>>>>>>>>>>> dupicious by now calling H to be a some sort of other >>>>>>>>>>>>>> decider).

    Since you claim that Halt-Decider-H "Correctly" returned >>>>>>>>>>>>>> false for H(D,D) we know that D(D) Halts, so D the problem >>>>>>>>>>>>>> of D has an answer so hard to call "undecidable"

    Again, what is the definition of your "Language", and why >>>>>>>>>>>>>> do you call {H,D} as UNDECIDABLE, since H will be a FIXED >>>>>>>>>>>>>> DEFINED decider that is just WRONG about its input, that >>>>>>>>>>>>>> isn't "undecidable".

    {H,D} undecidable means that D is undecidable for H, which >>>>>>>>>>>>> is an
    verified fact. The set of {H,*} finite string pairs do >>>>>>>>>>>>> define a
    language.  Decidability <is> a semantic property because it >>>>>>>>>>>>> can only be correctly decided on the basis of behavior. >>>>>>>>>>>>>

    What do you mean by "Undecidable by H?"


    H correctly determines that it cannot provide a halt status >>>>>>>>>>> consistent with the behavior of the directly executed D(D). >>>>>>>>>>
    So? If it REALLY could detect that, it just needs to give the >>>>>>>>>> opposite answer.

    Or, in other words, you are just admitting that H is wrong. >>>>>>>>>
    Try and show how D could do that.
    D can loop if H says it will halt.
    D can halt when H says it will loop.

    How does D make itself decidable by H to contradict
    H determining that it is undecidable?



    It doesn't need to, and the fact you are asking the question
    jkust shows you don't understand what you are talking about.

    You clearly don't understnad what "Decidability" means.



    *Computable set*
    In computability theory, a set of natural numbers is called
    computable,
    recursive, or decidable if there is an algorithm which takes a
    number as
    input, terminates after a finite amount of time (possibly
    depending on
    the given number) and correctly decides whether the number
    belongs to
    the set or not. https://en.wikipedia.org/wiki/Computable_set

    Because A finite string can be construed as a very large integer the >>>>>>> above must equally apply to finite strings. That you are trying to >>>>>>> get away with disavowing this doesn't seem quite right. Since you >>>>>>> only
    have an EE degree we could chalk this up to ignorance.

    It does seem that you acknowledge that there is no way to make
    decidability undecidable.



    Except that "Decidability" isn't a property of an "input"/Machine, >>>>>> but of a PROBLEM, or one of the sets you are talking about. (not
    MEMBERS of the set, which are the machines, but the set as a whole)> >>>>>>
    So, you are confusing a property of the SET with a property of the >>>>>> members.

    Decidability is about the ability for there to exist a machine
    that can decide if its input is a member of the set. If there
    exist such a machine, then the SET is computable/decidable. If
    not, the SET isn't computable/decidable.


    Since I just quoted that to you it is reasonable that you accept it.

    Nope, Decidability is a property of PROBLEMS or SETS, not INPUTS.

    You can't seem to tell the diffence bcause of your ignorance.


    Nothing he talks about the possible members themselves being in
    the set or not being a property like "decidable", it just isn't a
    property of the members.


    Using Rogers' characterization of acceptable programming systems,
    Rice's
    theorem may essentially be generalized from Turing machines to most
    computer programming languages: there exists no automatic method that >>>>> decides with generality non-trivial questions on the behavior of
    computer programs. https://en.wikipedia.org/wiki/Rice%27s_theorem

    Yes, it doesn't need to be about Turning Machines, but it is still
    about the ability to create a "program" to compute a Function /
    Decider for a Language/Set.


    H correctly determines whether or not it can correctly determine the >>>>> halting status for all of the members of the set of conventional
    halting
    problem proof counter-examples and an infinite set of other elements. >>>>
    But that isn't a proper property.

    You don't have "Decidability" on individual inputs, so it isn't a
    Property of the input that can be decided on.

    H divides inputs into halting decidable and halting undecidable.

    Which means?

    After all, *ALL* inputs have a definite halting state, so there is a
    correct answer to them, so there always exists a decider that will get
    the right answer.

    It seems by your attempt at a definition, a "Decider" that just
    decides all machines are non-ha;ting would have all halting machines
    defined as undecidable.

    I never said anything like that.
    (Here is what I already said)
    H returns three values:

    Answering WHAT question?
    The answers seem to be to two different questions.
    Since the input IS either Halting or Not Halting, if H is supposed to be
    a Halt Decider, your 0 below is NEVER a correct answer/


    0=halting is undecidable by H
    1=halting
    2=not halting

    The human user runs H(D,D) and H returns 0. This tells the human
    user to run H1(D,D) to get the correct halt status decision for H.
    Because D could not have reconfigured itself this must work correctly.

    But H can't know who is running it. That is part of the definition of a Computation.

    Also, by definition, the "Halt Decider" is the FULL PROCEDURE" used to
    decide halting, thus H^/P/D does EXACTLY the same steps as "The User" to
    get the answer.

    That is call H(D,D), and if it returns 0, call H1(D,D) and then do the opposite, if not, do the opposite of what H returned.

    THAT is the definition of D, and if you can't code that, then your input
    set isn't Turing Complete, so your decider fails there. If you can write
    that, the final answer you got from above will be wrong.

    The fact that you still seem to think that D is built just on H means
    you don't understand the rules of the problem.

    "H" in the proof, is the COMPLETE Halt Decider, not your function H
    which no longer fills that role. Then H^/P/D is built to use that
    decider, and does the opposite.




    H is deciding the semantic property of its own behavior on a set of
    finite strings. The above says this can be done in C.

    Nope, just shows you don't understand a thing about what you are
    saying.

    Any idiot can say that. Provide both reasoning and sources.





    Your question is like asking if 2 is Purple.

    Mere empty rhetoric utterly bereft of any supporting reasoning.



    Nope, since "Decidability" isn't a property of a given input, trying
    to ask if a given input is Decidable is a simple category error.


        Decidability is about the ability for there to exist a machine
        that can decide if its input is a member of the set.

    H decides an infinite set of elements that are halting decidable for H
    and another set that are halting undecidable for H.

    Again, "Halting Decidable" is an improper term,

    It is a brand new concept that was never relevant before because
    everyone incorrectly assumed that deciding halting decidability
    was blocked by Rice.


    And shows how deceptive you are acting, and how ignorant, as what you
    are trying to call "Decidable" has no actual relation to the word as use.

    H correctly divides its inputs into those having the pathological relationship to H of the conventional halting problem proofs and
    inputs that do not have this relationship.

    Except that it can only do that to the not-Turing-Complete subset that
    it can accept (since you define that D can't have its own copy of H, and
    that D can't actually make a proper copy of its input to something that
    would be writable).

    Then, it also has no bearing on the actual problem, since it doesn't use
    the correct definition of Halting, so just is making a claim that POOP
    deciders might be possible, but says nothing about actual Halt Deciders.


    as ALL machines are "Decidable" to halt by some machine. So there does
    exist a machine that will give the right answer. It is sometimes a
    different machine for different inputs.

    Read that definition again, and perhaps find a better source, as
    decidability is the ability for there to exist a machine that can
    decider FOR ANY INPUT, if that input is a member of the set.


    My current code can already do that for every member of the set.

    But the set it is deciding on isn't Turing Complete, and doesn't
    actually align to the actual definition of "Decidable".


    There ALWAYS exist a machine that will correctly indicate if a
    SPECIFIC input is a member of the set. Trivially, it can be one of two
    possible machines, Machine 1 always answers YES, Machine 2 always
    answers no. One of those machines is right. The key point is that you
    need to determine the answer for ALL inputs, thus it isn't a property
    of one of the inputs, but of the SET.


    My code also rejects inputs that are not members of this set.

    But the set it is deciding on isn't Turing Complete, and doesn't
    actually align to the actual definition of "Decidable".



    As it is a property of the SET and not an input, there can't be
    'decider' to determine if an 'input' has that property, since inputs
    don't have that property, the set they are being tested for does.


    I had very recent very long discussions with a PhD computer scientist
    and he seemed to believe that the halting problem is about dividing
    finite string pairs into those that halt on their input and those that
    do not.

    It is about those strings that represent machines that Halt and those
    that don't. It can also be expressed a whose CORRECT simulation Halts or
    not. Note, "Correct Simulation" in this context implies a simulation
    that matches the FULL .behavior of the machine described, and thus not
    one that is aborted


    My case is analogous. H divides finite strings into those that have a pathological relationship to H and those that do not on the basis of the behavior that this finite string specifies.


    But the set it is deciding on isn't Turing Complete, and doesn't
    actually align to the actual definition of "Decidable".


    Your inability to understand that just highlights how ignorant you
    are of the whole field.

    I suspect that you might not have more than bluster and a penchant for
    rebuttal.


    Really, I guess that is just you projecting, because you describe
    yourself to the tee.





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